In those days the X rays were registered by special photographic film, developed in much the same way that ordinary photographic negatives are developed. Nowadays the X rays are caught and measured by counters. A special camera had to move the crystal in the beam, and the X-ray film with it, in order to record a particular portion of the diffraction data at a time.
Although I must have learned all this when I took my B.Sc. in physics, I had forgotten most of it by this time, so that I could get only a rough idea of what Perutz had been doing. I learned that protein crystals usually had a lot of water in them, tucked away in the interstices in the crystal between one large molecule and its neighbors. In a drier atmosphere a crystal could shrink somewhat, as the protein molecules packed more closely together, and it was these shrinkage stages that Perutz had been studying. If the atmosphere were too dry, the packing of the molecules would become jumbled, as the bulky molecules vainly tried to get as near together as possible. The nice X-ray diffraction pattern, with many sharp discrete spots, would then deteriorate to a few smudges on the X-ray film. In diffraction, regular three-dimensional structures produce a whole series of discrete spots, as Bragg had explained many years before.
I also knew about the major problem of X-ray crystallography. Even if the strength of all the many X-ray spots were measured (in those days a tremendous undertaking) and even if the atoms in the crystals were so regular that those X-ray spots corresponding to fine details were also recorded, the mathematics showed clearly that the spots contained just half the information to reveal the three-dimensional structure. [In technical terms the spots gave the intensities of all the many Fourier components but not their phases.] If by some magic the position of each atom were known, then it was possible (though in those days very laborious) to calculate exactly what the X-ray diffraction pattern would look like, and also to calculate the missing information—the phases. But given only the spots, the theory showed that very, very many possible three-dimensional arrangements of electron density could give exactly the same spots, and there was no easy way to decide which was the correct one.
In recent years it has been shown, mainly by the work of Jerome Karle and Herbert Hauptman, how to do this for small molecules by putting various rather natural constraints into the mathematics. For this work they were awarded the Nobel Prize for Chemistry in 1985. But even today such methods cannot, by themselves, be used for large molecules of the size of most proteins.
Thus it was not surprising that in the late 1940s Perutz had not progressed very far. I listened carefully to his explanation of his work and even ventured a few comments. This must have made me appear more perceptive and quicker on the uptake than I really was. In any event, I impressed Perutz sufficiently for him to welcome the idea of my joining him, provided the MRC would support me.
In 1949 Odile and I got married. We had first met during the war when she was a naval officer—strictly speaking a WREN officer (the British equivalent of the WAVES, the women’s naval service). Toward the latter part of the war she worked at the Admiralty headquarters in Whitehall (the main government street in London), translating captured German documents. After the war she became an art student again, this time at St. Martin’s School of Art, in Charing Cross Road, not far from Whitehall. I was then working in Whitehall myself, in Naval Intelligence, so it was easy for us to meet. In 1947 Doreen and I were divorced. Odile had transferred to a new course in fashion design at the Royal College of Art, but after the first year she decided she preferred marriage to further study.
We spent our honeymoon in Italy. Only after we returned did I discover that the First International Congress of Biochemistry had taken place in Cambridge while we were away. In those days there were nothing like as many scientific meetings as there are now. As a beginner in research, still almost an amateur, I was not especially aware of even those meetings that did take place. I think at the back of my mind was the idea that science was an occupation for gentlemen (even if somewhat impoverished gentlemen). Incredible as it may seem, I had not realized that for many it was a highly competitive career.
The Perutzes had lived for some time in a tiny furnished apartment very conveniently located near the center of Cambridge and only a few minutes’ walk from the Cavendish. They now planned to move into a suburban house, to have more room, and suggested to us that we might take their place. We were delighted with the idea and moved into The Green Door, as it was called, a set of two and one-half rooms and a small kitchen, at the top of The Old Vicarage, next to St. Clement’s church on Bridge Street, between the top of Portugal Place and Thompson’s Lane. The owner, a tobacconist, and his wife lived in the main body of the house while we occupied the attic. The actual Green Door was on the ground floor, at the back, leading to a narrow staircase that went up to our set of rooms. The washbasin and lavatory were halfway up these stairs and the bath, covered by a hinged board, was tucked into the small kitchen. It was often necessary to move a miscellaneous collection of saucepans and dishes if one wanted to have a bath. One room served as a living room, the other as a bedroom, while the smallest room was used as a bedroom for my son Michael, when he came home for the holidays from his boarding school.
Odile and I had our leisurely breakfasts by the attic window in the little living room, looking out over the graveyard to Bridge Street and beyond that to the chapel of St. John’s College. There was much less motor traffic in those days, though many bicycles. Sometimes in the evening we would hear an owl hooting from one of the trees that bordered the college. We had only a small income but fortunately the rent was also very small, even though the apartment was rented furnished. The landlord apologized profusely when he felt compelled to raise our rent from thirty shillings a week to thirty shillings and sixpence. Odile luxuriated in her newly found leisure, read French novels in front of the small gas fire, and attended, informally, a few lectures on French literature, while I reveled in the romance of doing real scientific research and in the fascination of my new subject.
The first thing I had to do was to teach myself X-ray crystallography, both the theory and the practice. Perutz advised me which textbooks to read and I was shown the elements of mounting crystals and taking X-ray pictures. Simple inspection of parts of the X-ray diffraction pattern usually gave, in a fairly straightforward manner, not only the physical dimensions of the unit cell—the spatial repeat unit—but also revealed something about its symmetry. Because biological molecules often have a “handedness"—their mirror image is not usually found in living things—certain symmetry elements [inversion through a center, reflection, and the related glide planes] cannot occur in protein crystals. This limitation reduces drastically the possible number of symmetry combinations, or space groups, as they are called.
There is also a well-known limitation on rotation axes. Wallpaper can have a twofold rotation axis—it looks exactly the same if it is rotated by 180 degrees—or a threefold, fourfold, or sixfold one. All other rotational axes are impossible, including a fivefold one. This restriction is true for any extended pattern with two-dimensional symmetry, known as a plane group, and thus also for three-dimensional extended symmetry, or a space group. Of course a single object can have fivefold symmetry. The regular dodecahedron and icosahedron, which have fivefold rotational axes, were known to the Greeks, but what is allowed for a point group (which has no dimensions) is impossible for a plane group (of two dimensions) or a space group (of three dimensions). Moslem art, which for religious reasons is forbidden to depict people or animals (since the Prophet was very hostile to paganism), is often for this reason very geometrical in design. One can sometimes see the artist flirting with local fivefold symmetry without ever attaining it on a repeating basis. As it turns out, the protein shells of many small “spherical” viruses (such as the polio virus) usually have fivefold symmetry, but that is another story.
The theory of the X-ray diffraction of crystals is straightforward, so much so that most modern physicists find it rather dull. Although
it is necessary to be able to handle the algebraic details, I soon found I could see the answer to many of these mathematical problems by a combination of imagery and logic, without first having to slog through the mathematics.
Some years later, when Jim Watson joined us at the Cavendish, I used some of these visual methods, based on the deeper mathematics, to teach him the outlines of X-ray diffraction. I even considered writing a small didactic monograph on it, to be entitled “Fourier Transforms for Bird Watchers” (Jim had become a biologist because of an early interest in bird-watching), but there were too many other distractions and I never wrote it.
At that time there was no easily available textbook along these lines. The existing texts usually used a step-by-step method, based largely on Bragg’s law and the historical development of the subject. To someone like myself this only made it more difficult and certainly more tedious, since an elementary method often arouses deeper questions in the learner and these worries can impede one’s progress in learning. It is often better, at least for the brighter pupils, to go straight to the advanced treatment and try to get over the more powerful formalism while at the same time attempting to provide some insight into what is going on. In my case there was no alternative but to teach X-ray diffraction to myself. This was useful as I acquired a fairly thorough and intimate knowledge of it. Moreover, because Perutz was studying the shrinkage stages of a crystal made of large molecules, I learned how to deal with diffraction from a single molecule, and only then arranged them in a regular crystal lattice, rather than following the more conventional path of starting off with them in a lattice. This proved valuable to me later.
Armed with this new knowledge, I reread Perutz’s papers and spent some time thinking about how the problem of protein structure was to be solved. Perutz had tentatively suggested that the shape of the molecule was somewhat like an old-fashioned lady’s hatbox, and he had put such a diagram into his first paper. (Incidentally, diagrams of models are often difficult to draw satisfactorily, since, unless care is taken, they usually convey more than one intends.) For various reasons I thought that the hatbox was implausible, and I tried to find evidence for other possible shapes. Remember that the relevant X-ray data could not by itself tell us the shape, but that any proposed shape could be used to calculate the X-ray data. The shape influences only the few X-ray reflections that correspond to the coarse structure of the crystal. Their strength depends on the contrast between the high electron density of the protein and the lower electron density of the “water” (actually a salt solution) in between the molecules. Even if such a low-resolution picture of the electron density were available, it would not immediately give the shape of a single molecule, since at various places the protein molecules are in close contact. Where one molecule finished and the next began could not be seen. Fortunately Perutz had studied a set of similar packings—the several shrinkage stages—and by assuming that protein molecules are relatively rigid and merely packed together a little differently in the different stages, the range of possible shapes could be restricted.
I made some progress with the main problem but eventually became stuck. Meanwhile Bragg had independently thought about it. Whereas I had gotten bogged down, he made rapid progress. He boldly assumed that one could approximate the shape by an ellipsoid—a particularly simple type of distorted sphere. Then he looked at what little was known of the crystals of hemoglobin of other species of animal, on the assumption that all types of hemoglobin molecules were likely to have about the same shape. Moreover, he was not disturbed if the data did not exactly fit his model, since it was unlikely that the molecule was exactly an ellipsoid. In other words he made bold, simplifying assumptions; looked at as wide a range of data as possible; and was critical but not pernickety, as I had been, about the fit between his model and experimental facts. He arrived at a shape that we now know is not a bad approximation to the molecule’s real shape, and he and Perutz published a paper on it. The result was not of first-class importance, if only because the method was indirect and needed confirmation by more direct methods, but it was a revelation to me as to how to do scientific research and, more important, how not to do it.
As I learned more about the main problem, I began to worry about how it might be solved. As I have said, the X-ray data contained just half the necessary information, though it was known that some of what was available was probably redundant. Was there any systematic way to use the available data? It turned out there was. Some years earlier a crystallographer, Lindo Patterson, had shown that experimental data could be used to construct a special density map, now called a Patterson. [All the amplitudes of the Fourier components are squared and all the phases are put to zero.]
What did this density map mean? Patterson showed that it represented all the possible interpeak distances in the real electron density map, all superimposed, so that if the real density map frequently had high density a distance of 10 Å apart in a certain direction, then there would be a peak at 10 Å from the origin in the appropriate direction in the Patterson map. (One Ångstrom unit is equal to one ten-billionth of a meter.) In mathematical terms, this would be a three-dimensional map of the autocorrelation function of the electron density. For a unit cell with very few atoms in it, and using high-resolution X-ray data, one could sometimes unscramble this map of all the possible interatomic distances and obtain the real map of the atomic arrangements. Alas, for protein there were far too many atoms and the resolution was too poor, so that doing this was quite hopeless. Nevertheless, strong features in the Patterson could hint at broad features in the atomic arrangements, and indeed Perutz had predicted that the protein was folded to give rods of electron density, lying in a particular direction, because he saw rods of high density in that direction in the Patterson. As it turned out the latter rods were not really as high as he had imagined (he had at that time only the relative intensity of his X-ray spots, not their absolute value) so the folding was not quite as simple as he had conjectured.
This calculation of the Patterson of his crystals of horse hemoglobin was a difficult and laborious piece of work, since in those days the methods, both for collecting X-ray data and for calculating Fourier Transforms, were, by modern standards, primitive in the extreme. Many crystals had to be mounted (since each would only take a certain dose of X rays before deteriorating); many X-ray photos had to be taken, cross-calibrated, measured by eye, and systematic corrections made. The calculations were not done on what we would now call a computer (that came later) but using an IBM punched card machine. They took an assistant three months and were very laborious. Then all the numbers obtained had to be plotted and contours drawn, till eventually one ended up with a stack of transparent sheets, each having a section of the Patterson density shown on them as contours. As I recall, the negative contours (the average correlation was taken as zero) were omitted and only the positive ones plotted.
I received another lesson when Perutz described his results to a small group of X-ray crystallographers from different parts of Britain assembled in the Cavendish. After his presentation, Bernal rose to comment on it. I regarded Bernal as a genius. For some reason I had acquired the idea that all geniuses behaved badly. I was therefore surprised to hear him praise Perutz in the most genial way for his courage in undertaking such a difficult and, at that time, unprecedented task and for his thoroughness and persistence in carrying it through. Only then did Bernal venture to express, in the nicest possible way, some reservations he had about the Patterson method and this example of it in particular. I learned that if you have something critical to say about a piece of scientific work, it is better to say it firmly but nicely and to preface it with praise of any good aspects of it. I only wish I had always stuck to this useful rule. Unfortunately I have sometimes been carried away by my impatience and expressed myself too briskly and in too devastating a manner.
It was at such a seminar that I gave my first crystallographic talk. Although I was over thirty it was only the second researc
h seminar I had ever given, the first having been about moving magnetic particles in cytoplasm. I made the usual beginner’s mistake of trying to get too much into the allotted twenty minutes and was disconcerted to see, after I was about halfway through, that Bernal was fidgeting and only half paying attention. Only later did I learn that he was worrying about where his slides were for the talk he was to give following mine.
All this was of little consequence compared to the subject of my talk, which, broadly speaking, was that they were all wasting their time and that, according to my analysis, almost all the methods they were pursuing had no chance of success. I went through each method in turn, including the Patterson, and tried to demonstrate that all but one was quite hopeless. The exception was the so-called method of isomorphous replacement, which I had calculated had some prospect of success, provided it could be done chemically.
As I mentioned earlier, X-ray diffraction data normally gives us only half the information we need to reconstruct the three-dimensional picture of the electron density of a crystal. We need this three-dimensional picture to help us locate the many thousands of atoms in the crystal. Is there any means of obtaining the missing part of the data? It turns out there is. Suppose a very heavy atom, such as mercury, can be added to the crystal at the same spot on every one of the protein molecules it contains. Suppose this addition does not disturb the packing together of the protein molecules but only displaces an odd water molecule or two. We can then obtain two different X-ray patterns: one without the mercury there, and one with it. By studying the differences between the two patterns we can, with luck, locate where the mercury atoms lie in the crystal [strictly, in the unit cell]. Having found these positions, we can obtain some of the missing information by seeing, for each X-ray spot, whether the mercury has made that spot weaker or stronger.
What Mad Pursuit Page 6